Question

A market researcher collects a simple random sample of customers from a population of over a million​ customers that use a home improvement website. After analyzing the​ sample, she states that she has​ 95% confidence that the mean​ time customers spent on​ that website per day is between 20 and 58 minutes. Suppose that the population mean​ time customers spent on that website is 31 minutes a day. Does this value of the population mean help to show that the confidence interval estimate is​ correct? Explain. Choose the correct answer below. A. ​Yes, because the population​ mean, mu is within​ 95% of the midpoint of the confidence interval estimate. B. No​, because the population​ mean, mu​, is not included within the confidence interval estimate. C. Yes​, because the population​ mean, mu​, is included within the confidence interval estimate. D. ​No, because the population​ mean, mu​, is not the midpoint of the confidence interval estimate. E. No comma because the population mean comma mu comma is not in the middle half of the confidence interval estimate

Answer 1

Explanation:

The confidence interval gives an estimate of range of values that could possibly contain the unknown population parameter which could be the population mean or population standard deviation.

Given that the lower end of the confidence interval is 20 minutes and the upper end of the confidence interval is 58 minutes, if the population mean​ time customers spent on that website is 31 minutes a day, then the correct option is

C. Yes​, because the population​ mean, mu​, is included within the confidence interval estimate.